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ii) div grad ƒ = V²f = Af, (A : Laplace Operatörü) v) grad(fg) = g grad(f) + ƒ grad(g) %3D

ii) div grad ƒ = V²f = Af, (A : Laplace Operatörü) v) grad(fg) = g grad(f) + ƒ grad(g) %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve only (iii) and (iv).

(a) Show that the following identities are correct. (i) div rot A = 0 (ii) rot grad f = 0 (iii) div grad f = V²ƒ = Aƒ, (A: Laplace Operatörü) (iv) grad(fg) = g grad(f) + f grad(g) (v) div(ƒÃ) = f div Ã+ grad(f).à (vi) rot(fÃ) = f rot Ã+ grad(f) × rot à (vii) div(Ã × B) = B. rot à – Ã. rot B (viii) rot rot A = grad div à – AÃ
Transcribed Image Text:(a) Show that the following identities are correct. (i) div rot A = 0 (ii) rot grad f = 0 (iii) div grad f = V²ƒ = Aƒ, (A: Laplace Operatörü) (iv) grad(fg) = g grad(f) + f grad(g) (v) div(ƒÃ) = f div Ã+ grad(f).à (vi) rot(fÃ) = f rot Ã+ grad(f) × rot à (vii) div(Ã × B) = B. rot à – Ã. rot B (viii) rot rot A = grad div à – AÃ
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